Given: Mean = 550, standard deviation = 45, scores 560 and 580.
Formula: [tex] z = \frac{x-xbar}{SD} [/tex]
Result: [tex] z_{560} = 0.2222 {\,} z_{580} = 0.6666[/tex]
Go to a z score table and get probabilities associated with these z scores.
[tex] p_{560} = 0.5871 {\,} p_{580} = 0.7486 [/tex]
Note: More exact answers can be obtained via a stats calculator or Excel.
Final Answer: 0.7486 - 0.5871 = 0.1615 or 16.15%
Jeff
